Abstract

We describe and analyze a method by which an optical polarization state is mapped to an image sensor. When placed in a Bayesian framework, the analysis allows a priori information about the polarization state to be introduced into the measurement. We show that when such a measurement is applied to a single photon, it eliminates exactly one fully polarized state, offering an important insight about the information gained from a single photon polarization measurement.

Figures (5)

Experimental setup, in which a partially-polarized beam is prepared by combining two orthogonally polarized laser beams, spatially filtering and recollimating them. This beam then passes through the center of the SEO element shown in the inset, and through a left-circular analyzer, and is focused by a lens onto a CCD. (a) Experimental image of contours of equal (half-wave) birefringence of the SEO. (b) Theoretical model of birefringence at the central region of the SEO. The aperture size used in the experiments, corresponding to cR = 0.8π, is illustrated with the small blue circle in the inset.

(a,b) Plots of P(xn|s) (with black corresponding to zero) for given xn as a function of s, over a cross-section of the Poincaré sphere that includes the origin as well as the points of zero and maximum probability, for (a) ū = 0 and (b) ū = (0, 0, 0.5). (c) Plot of q(s) over the surface of the sphere for the case of two detected photons.

Widths of the standard deviations of the polarization measurements corresponding to several values of s0 within the s1–s3 slice of the Poincaré sphere, for (a) the proposed SEO-based polarimetric system, (b) for the optimal polarimeter; and (c) for a standard polarimeter. The radius of the green circles represents the extent of the standard deviation in the direction normal to the plane.

Metrics

Table 1

Measured polarization states for the PSFs in Fig. 5. The right hand columns show: root sum square (RSS) difference when compared to a commercial polarimeter; equivalent volume uncertainty; difference in the degree of polarization (ΔDoP); measured DoP.